Sketch the distribution and show its mean and standard deviation. Hint: To find

Question

Sketch the distribution and show its mean and standard deviation. Hint: To find the standard deviation, think Empirical Rule covered in Week 1

"SuperFun expects to sell Weather Teddy for $24 based on a cost of $16 per unit. If inventory remains after the holiday season, SuperFun will sell all surplus inventories for $5 per unit. After reviewing the sales history of similar products, SuperFun’s senior sales forecaster predicted an expected demand of 20,000 units with a 95% probability that demand would be between 10,000 units and 30,000 units."

Answer the question based on the following data set:

Order Quantity      20,000 Purchase Cost per unit $    16.00 Sales Order Quantity Total Cost Total Revenue Profit @ $24.00 @ $5.00 Pessimistic 10,000             20,000 Likely 20,000             20,000 Optimistic 30,000             20,000

Explanation / Answer

Here,

sales price P = $ 24

Cost price C = $ 16

Salvage value S= $ 5

Underage cost = P- S = 24 - 16 = $ 8

Overage cost = C - S = $ 16 - $ 5 = $ 11

So, as we have to find the optimal order quantity. Qoptimum

Here Pr(Q < Qoptimum ) = F [underage cost/ (overage cost + underage cost)] = F(8/19)

Here, 95% probability that demand would be between 10,000 units and 30,000 units. So, here demand is 20000. As per empirical rule the standard deviation the llimits are 2 standard deviation away.

Standard deviation = $ 5000

Pr(Q < Qoptimum ) = F(8/19) = 0.4211

so Z value related to given p - value = 0.4211

Z = -0.2 = (Qoptimum - 20000)/ 5000

Qoptimum = 20000 - 0.2 * 5000 = 19000

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